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41

Dec 31, 2013
12/13

by
Patrick Bruskiewich

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An original poem by Patrick Bruskiewich Have compassion for us! compassion for we the adventurous for our errors, for our sins. They are Apollinaire in nature.

Topics: poem, mathematics, Canadian poetry

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106

Dec 30, 2013
12/13

by
Patrick Bruskiewich

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An original poem by Patrick Bruskiewich The Great One he stood And drew back his dark hood It is Pythagoras, our oracle With another of his miracles.

Topics: poem, mathematics, Canadian poetry

50
50

Jun 12, 2015
06/15

by
Patrick Bruskiewich

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This is a short excerpt from the book Blaise Pascal and his Passion for Polynomials. The excerpt talks about Pascal being born prematurely, and as a result having a high I.Q. and attendant health difficulties. The book is available through Amazon / Kindle

Topics: Blaise Pascal, high I.Q., precociousness, brilliance, mathematics

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132

Dec 28, 2013
12/13

by
Patrick Bruskiewich

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In reading J.R. Taylor's 1983 article Euler, the Master Calculator a small commentary is in order about one of the mathematics questions not fully explained by Euler. In his 1983 article titled Euler, the Master Calculator J.R. Taylor presented eight examples of the type of mathematics that Euler became famous for. Taylor implies that one of the eight examples was not fully elucidated by Euler, to simply ln ln ln e^(1/e) which in the surface appears to lead to an inconsistency within the...

Topics: Euler, exponential function, natural logarithm, mathematics, mathematician

106
106

Dec 25, 2013
12/13

by
Patrick Bruskiewich

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Prime Numbers are of fundamental importance to number theory. The most direct way to find Prime Numbers is to use an algorithm, such as the Sieve of Eratosthenes. There is a simple algorithm, or Sieve, involving Prime Number Strings which will be presented in this short paper.

Topics: Prime Number, Algorithm, Prime Number String, Sieve, mathematics

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218

Nov 17, 2014
11/14

by
Patrick Bruskiewich

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The Magic of Numbers: Chapter One â with Guided Notes by Eric Temple Bell Transcribed and annotated by Patrick Bruskiewich Excerpt from The Magic of Numbers. The entire book, complete with Guided Notes is available in three volumes through Amazon Â© Patrick Bruskiewich 2014, Vancouver, BC, Canada All rights reserved. This excerpt, or any part thereof, must not be reproduced in any form without the written permission of the author. The author can be contacted through Amazon.

Topics: Mathematics, Pythagoras, Magic of Numbers, Eric Temple Bell, Guided Notes

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117

Dec 29, 2013
12/13

by
Patrick Bruskiewich

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Most students are introduced to the Harmonic Series and are told it yields an infinite sum, and then things are left at that. There is something beautiful in taking the next step, which is to introduce the Euler Constant. Unfortunately thus next step is not always done. This little article was lost amongst the author's notes in 1983 and only recently found in a box of old manuscripts. There will be other A Little Bit of Euler articles.

Topics: Euler, Euler's Constant, Harmonic Series, natural logarithm, mathematics, mathematicians

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189

Dec 26, 2013
12/13

by
Patrick Bruskiewich

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There is a story of G.H. Hardy visiting his friend Srinivasa Ramanujan while the later was hospitalized and offering his friend the comment that he arrived in cab 1729. Lacking any topic of conversation Hardy made mention that the number 1729 was "uninteresting." Ramanujan's rejoinder that 1729 being the smallest sum of two cubes that can be expressed in two ways is now legendary. For someone like Ramanujan whose brain was wired for mathematics, his was a prepared mind that stated the...

Topics: Ramanujan, Hardy, 1729, sum of two cubes, mathematics, mathematicians

808
808

Dec 30, 2013
12/13

by
Patrick Bruskiewich

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In this little paper I have collected some quotes from A Mathematician's Apology by G.H. Hardy, Cambridge University Press, 1967. This little article was lost amongst the author's notes in 1983 and only recently found in a box of old manuscripts.

Topics: G.H. Hardy, Quotes from A Mathematician's Apology, mathematics, creativity, life in general,...

202
202

Dec 31, 2013
12/13

by
Patrick Bruskiewich

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To simplify an integral that is a rational function in cos(x) or sin(x), a substitution of the form t= tanâ¡(ax/2) will convert the integrand into an ordinary rational function in t. This substitution, is known as the Weierstrass Substitution, and honours the mathematician, Karl Weierstrass (1815-1897) who developed the technique. In this short paper the integrals for sine and cosine are solved using the Weierstrass Substitution

Topics: Weierstrass Substitution, Integration, Calculus, mathematics, mathematician, cosine, sine, rational...

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3.0

Oct 5, 2017
10/17

by
Patrick Bruskiewich

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In this short paper I derive a symmetrized formula for the volume of the frustrum of a truncated Rectangular Pyramid, as well as for a Right Cone and an Ellipsoidal Cone. In a modern sense, symmetrization is an idée fixe in both mathematics and mathematical-physics. I have looked though all my math books and have yet to come across this symmetrized expression and so I have decided to name it The Bruskiewich Symmetrized Formula for Truncated Volumes.

Topics: truncated volume, mathematics, right pyramid, rectangular pyramid, right cone, ellipsoidal cone,...

189
189

Dec 28, 2013
12/13

by
Patrick Bruskiewich

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To simplify an integral that is a rational function in cos(x) or sin(x), a substitution of the form t = tan(ax/2) will convert the integrand into an ordinary rational function in t. This substitution, is known as the Weierstrass Substitution, and honours the mathematician, Karl Weierstrass (1815-1897) who developed the technique.

Topics: Weierstrass Substitution, Integration, Calculus, mathematics, mathematician, cosine, sine, rational...

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251

Mar 26, 2013
03/13

by
Patrick Bruskiewich

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We can view reflection of light off a mirror, and refraction of light leading to Snell's Law as a Time Optimization Problem (TOP). Fermat's Principle is that the path traveled by light is the path of least travel time, an explicit description of time optimization. A third TOP problem, flight time between two points, with auxiliary travel constraints, will also be considered in this paper. Solving Time Optimization Problem using a spreadsheet program like EXCEL is a good example of...

Topics: Time Optimization, reflection, refraction, Snell's Law, Fermat's Principle, Mathematics-Based...

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247

Nov 15, 2012
11/12

by
Patrick Bruskiewich

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In mathematical physics a number of specialized techniques are learned with the passage of time, techniques which become part of an applied physicist's box of magic. One technique is colloquially known as "Boot Strapping", by which a minimum of data can be used to yield a maximum of results. Sometimes this involves taking a series of under described equations (say a single equation in two unknowns), some additional good data points and a technique to more fully analyze the problem. In...

Topics: physics, mathematics, boot strap technique, freshman physics example, seismic imaging, reflection,...

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173

Jan 20, 2013
01/13

by
Patrick Bruskiewich

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This manuscript was co-written in 1982 with Dr. George Volkoff but remained lost in the primary author's papers, until recently rediscovered with other manuscripts. The crux of this paper stems from discussions that the primary author had with Dr. Volkoff, and prior discussions George had with his colleagues Stanislaw Ulam and the late John von Neumann. Using the Ulam Mapping Function an algorithm is developed to produce pseudo-random two and three state selection, such as coin tosses and...

Topics: Bruskiewich Volkoff Von Neumann Algorithm, George Volkoff, John von Neumann, Stanislaw Ulam,...

1,050
1.1K

Jul 30, 2016
07/16

by
George Polya

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This is George Polya's classic book How To Solve It.

Topics: mathematics, math, questions, how to solve it, Polya